Computational Mechanics of Fracture and Fatigue in Composite Laminates by Means of XFEM and CZM

This thesis is on the computational fracture analysis of static and fatigue fracture in advanced composite materials using Extended Finite Element Method (XFEM). Both in analytical and numerical approaches, the techniques and procedures need adjustments to take account for numerous effects brought by the heterogeneous and orthotropic nature of the advanced composite materials. The frst part of this study is on the calculation of Energy Release Rate (ERR) for cracks in composite structures. J-Integrals are widely used in computational methods for the ERR evaluation however, they do not show consistency in structured materials when
the crack is close to the material interfaces. Furthermore, when J-Integrals are implemented in XFEM, the enrichment functions of the crack-tip and the interfaces create even more complications. The outcome of the first study clarified that the linear elastic fracture mechanic (LEFM) approach on its own suffers from the effects caused by the crack-tip singularity and the stress field definition at the crack-tip. Cohesive Zone Model (CZM) is selected as an alternative to prevent some of the complications caused by the material heterogeneity and the singularity at the crack-tip. In-spite CZM is a damage based approach, it can be linked to the LEFM which is particularly useful for fatigue modelling.
In the second part, the implementation of CZM in XFEM for quasi-static and fatigue modelling is presented. Unlike previous FE implementations of CZM [14, 136], the current approach does not include the undamaged material in the traction separation law to avoid enriching undamaged elements. For the high-cyclic fatigue model, a thermodynamically consistent approach links the Paris law crack growth rate to the damage evolution. A new numerical approach is proposed for the implementation of the CZM for quasi-static and fatigue fracture modelling in XFEM. The outcomes are then compared to the results of other experimental and numerical studies. The fatigue test results comply to the Paris law predictions however,
linking Paris law with the damage evolution in the cohesive zone is prone to produce errors since different parts of the cohesive zone undergo different degradation rates.